A115263 Correlation triangle for floor((n+2)/2).

1, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 4, 6, 4, 3, 3, 5, 7, 7, 5, 3, 4, 6, 10, 10, 10, 6, 4, 4, 7, 11, 13, 13, 11, 7, 4, 5, 8, 14, 16, 19, 16, 14, 8, 5, 5, 9, 15, 19, 22, 22, 19, 15, 9, 5, 6, 10, 18, 22, 28, 28, 28, 22, 18, 10, 6

Offset

0,4

Comments

Row sums are A096338. Diagonal sums are A115264. T(2n,n) is A005993. T(2n,n)-T(2n,n+1) is floor((n+2)/2)(1+(-1)^n)/2 (aerated n+1).

Links

Table of n, a(n) for n=0..65.

Formula

G.f.: (1+x)(1+xy)/((1-x^2)^2*(1-x^2*y^2)^2*(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*floor((k-j+2)/2)*[j<=n-k]*floor((n-k-j+2)/2)}.

Example

Triangle begins
1;
1,1;
2,2,2;
2,3,3,2;
3,4,6,4,3;
3,5,7,7,5,3;

Crossrefs

Sequence in context: A103183 A335898 A143901 * A055894 A350226 A362136

Adjacent sequences: A115260 A115261 A115262 * A115264 A115265 A115266

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 18 2006

Status

approved